Which of the following numbers is a factor of 104? ${5,9,10,13,14}$
Solution: By definition, a factor of a number will divide evenly into that number. We can start by dividing $104$ by each of our answer choices. $104 \div 5 = 20\text{ R }4$ $104 \div 9 = 11\text{ R }5$ $104 \div 10 = 10\text{ R }4$ $104 \div 13 = 8$ $104 \div 14 = 7\text{ R }6$ The only answer choice that divides into $104$ with no remainder is $13$ $ 8$ $13$ $104$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $13$ are contained within the prime factors of $104$ $104 = 2\times2\times2\times13 13 = 13$ Therefore the only factor of $104$ out of our choices is $13$. We can say that $104$ is divisible by $13$.